Looking at your second picture, the one the wires in your ceiling box, it appears to me that you have a red wire and a white wire that has turned brown (possibly due to heat build up or bad connection); to me the brown wire looks whiter further back. It looks like there is a similar discoloration toward the stripped end of the red wire.
Red, along with black, is generally a hot wire (in fact 3 conductor wires are black/red as hots and white as a neutral).
I would connect black on the light to red on the ceiling, and white on the light to "brown" on the ceiling.
In an ideal world the copper would be connected to ground. I see other wires in the box; does there happen to be a green or bare copper wire back there? If so, the base copper should connect to the light and the green screen I see in the first picture.
What material is the electrical box made of metal or plastic and how old is the house?